We argue that Landau-Fermi liquids do not have any gravity duals in the purely classical limit. We employ the logarithmic behavior of entanglement entropy to characterize the existence of Fermi surfaces. By imposing the null energy condition, we show that the specific heat always behaves anomalously. We also present a classical gravity dual which has the expected behavior of the entanglement entropy and specific heat for non-Fermi liquids. 1

We study the asymptotic Virasoro symmetry which acts on the near-horizon region of extremal four-dimensional black hole solutions of gravity theories with higher-derivative corrections, following the recently proposed Kerr/CFT correspondence. We demonstrate that its central charge correctly reproduces the entropy formula of Iyer-Wald, once the boundary terms in the symplectic structure are carefully chosen. Downloaded fromhigher derivative corrections were discussed in 10).* ) The higher-derivative contribution to the central charge of the asymptotic Virasoro algebra of AdS 3 was studied in 38) and 39). The former treated the diffeomorphism-invariant Lagrangian density, but used the field redefinition specific to three dimensions which rewrites arbitrary such Lagrangians to the Einstein-Hilbert term with scalar fields with higher-derivative interactions. The latter paper dealt the topologically massive gravity 40) in the canonical ADM formalism, more directly following the approach taken by Brown-Henneaux. 3) It would be instructive to redo their analyses using the covariant phase space method. * * ) The relationship between cohomological methods 15)-18) and the closely related covariant methods based on the linear equations of motion 41)-43) and covariant symplectic methods in first order theories 44), 45) are detailed in 18). at Ernst Mayr Library of the Museum Comp Zoology, Harvard University on July 18, 2015 http://ptp.oxfordjournals.org/ Downloaded from * )Here a corresponds to a trivial cocycle and can be absorbed to a redefinition of H 0 . One can determine a natural definition of the angular momentum H 0 = H ∂ ϕ by performing such change so that a becomes the standard −1, but we do not pursue this direction in this paper.at

We apply Brown-Henneaux's method to the 5D extremal rotating Kaluza-Klein black holes essentially following the calculation of the Kerr/CFT correspondence, which is not based on supersymmetry nor string theory. We find that there are two completely different Virasoro algebras that can be obtained as the asymptotic symmetry algebras according to appropriate boundary conditions. The microscopic entropies are calculated by using the Cardy formula for both boundary conditions and they perfectly agree with the Bekenstein-Hawking entropy. The rotating Kaluza-Klein black holes contain a 4D dyonic Reissner-Nordström black hole and Myers-Perry black hole. Since the D-brane configurations corresponding to these black holes are known, we expect that our analysis will shed some light on deeper understanding of chiral CF T 2 's dual to extremal black holes.

The Kerr/CFT correspondence is a holographic duality between a two dimensional chiral conformal field theory (CFT) and the very near horizon limit of an extremal black hole, which includes an AdS 2 structure. To understand the dual chiral CFT 2 , we apply the Kerr/CFT correspondence to a certain class of black holes embedded in string theory, which include the D1-D5-P and the Breckenridge-Myers-Peet-Vafa black holes, and obtain the correct entropies for the black holes microscopically. These have an AdS 3 structure in the near horizon geometry and an AdS 2 structure in the very near horizon geometry. We identified one of the two Virasoro symmetries in the nonchiral CFT 2 dual to the AdS 3 , i.e., in the AdS 3 =CFT 2 , with the Virasoro symmetry in the chiral CFT 2 dual to the AdS 2 , i.e., in the Kerr/CFT correspondence. We also discuss a way to understand the chiral CFT 2 dual to generic extremal black holes. A kind of universality for the very near horizon geometries of extremal black holes will be important for the validity of the Kerr/CFT correspondence. Based on this analysis, we propose that the Kerr/CFT correspondence can be understood as a decoupling limit in which only the ground states remain.